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Title: Hidden Markov models for continuous multivariate data with missing responses and dropout Authors:  Silvia Pandolfi - University of Perugia (Italy) [presenting]
Francesco Bartolucci - University of Perugia (Italy)
Fulvia Pennoni - University of Milano-Bicocca (Italy)
Abstract: A Hidden Markov (HM) model is proposed for longitudinal continuous data with missing responses and dropout. These models assume the existence of an unobservable process, which follows a Markov chain with a discrete number of hidden states, affecting the distribution of the observed outcomes. In particular, we consider multivariate continuous responses that, for the same time occasion, are assumed to be correlated, according to a specific variance-covariance matrix, even conditionally on the hidden states. For the analysis of such kind of data, the presence of missing observations represents a relevant problem since dropout or non-monotone missing data patterns may occur. We propose an approach for inference with missing data by exploiting the steps of the Expectation-Maximization algorithm on the basis of suitable recursions. The resulting algorithm provides exact maximum likelihood estimates of model parameters under the missing-at-random assumption (MAR). We consider three different types of missing patters: (i) missing responses to one or more outcomes in a given time occasion; (ii) missing observation at one occasion followed by a proper evaluation in the subsequent time occasion (intermittent missing patterns); (iii) dropout, namely missing observation due to the early termination from the trial. The proposed model allows us to identify latent or unobserved clusters of units with homogeneous behavior and to track their evolution in a dynamic perspective.